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# Work Done by Centrifugal Pump

## Work Done by Centrifugal Pump Moving Water

• Within the case of the centrifugal pump, work is done with the impeller on the water.
• Such expression to the work done by the impeller in the water is obtained by drawing velocity triangles above each inlet and also an outlet of the impeller.
• Some water enters the impeller radially through the inlet for the best efficiency of the pump which means this absolute velocity of water at the inlet produces an angle of 90° with a specific direction of motion of the impeller at the inlet.
• Hence angle α = 90° and vwi  = 0. Fig. shows that velocity triangles at the inlet also outlet tips of the vanes fixed to an impeller.

Let Work Done by Centrifugal Pump

• N  = Speed from the impeller in r.p.m.,
• D1 = Diameter of the impeller at the inlet,
• u1 = Tangential velocity of impeller at inlet, = (πD1N/60)
• D2 = Diameter of impeller at outlet,
• u2 = Tangential velocity of impeller at outlet = (πD2N/60)
• v1 = Absolute velocity from water at inlet,
• vr1 = Relative velocity from water at inlet,
• α = Angle made at absolute velocity (v1) at the inlet with the direction from the motion of the vane,
• θ = Angle made at relative velocity (vr1) at the inlet with the direction from the motion of the vane,
• and v2, vr2, β and ϕ are corresponding values at the outlet.
• While the water enters the impeller radially which means the absolute velocity from water at the inlet is in each radial direction and hence angle α = 90° also vw1 = 0.
• Some centrifugal pump is the reverse of a radially inward flow reaction turbine.
• Just in the case of a radially inward flow reaction turbine some work done by the water at the runner per second per unit weight of the water striking per second is given by,

=(1/g)[Vw1u1-Vw2u2]

Work is done by some impeller on some water per second per unit weight of water striking per second

= – [Work was done in a case from turbine]

= – (1/g)[Vw1u1-Vw2u2]

=(1/g)[Vw2u2+Vw1u1]

=(1/g)[Vw2u2] [As Vw2=0]

Work is done by impeller on water per second

=(w/g)[Vw2u2]

where,

W = Weight of water

= ρ x g x Q

Q = Volume of water

= Area x Velocity of flow

= πD1B1 x vf1

= πD2B2 x vf2

• B1 and B2 = width from the impeller at the inlet also the outlet
• vf1 and vf2 = velocities from flow at inlet also outlet.

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